More Geometry . . . . Please Help Me!! :(?
You can think of the ice cream in a well packed ice cream cone as a half of a sphere added to a cone. If the cone is 4.5 inches tall and 3 inches across, how much ice cream is in the cone? (Round your answer to the nearest 0.1 units.)
- 1 decade agoFavorite Answer
Volume of a cone: (1/3)*base*height
Volume of a sphere: (4/3)*pi*(radius^3)
First, find the volume in the cone. (1/3)*(2.25pi)*(4.5) = 10.6028752
***Base is pi*(radius^2), which is 2.25pi
Then, find the volume of the half sphere. (1/2)*(4/3)*pi*(3.375) = 7.06858347
***Radius is 1.5, so radius^3 is 3.375.
Add the two parts together, and you get 10.6028752+7.06858347 = 17.6714587
Round this to the nearest 0.1, and you get 17.7 inches cubed.
I hope this is right!
- 1 decade ago
Since the problem asks how much ice cream is in the cone. This would be the volume of the cone + the volume of the hemisphere that sits on top of the cone.
Formula for Volume of a cone:
V = 1/3(pi)( r^2)( h)
Formula for the volume of a hemisphere:
Add these two formulas together to get
V=1/3(pi)(r^2)(h) + 2/3 (pi)(r^3)
Substitute in vales and solve.
- bcdasLv 41 decade ago
First you need the formulas for the volumes:
1/2 Sphere: 1/2*(4/3*pi*r^3) = 2/3*pi*r^3
For this problem, plug in the numbers and add them together:
pi*(3/2)^2*4.5/3 (3/2 b/c radius is half the across distance) + 2/3*pi*(3/2)^3
(in in^3)Source(s): volume equations from Calculus 8th ed. by Larson, Hostetler, Edwards
- 1 decade ago
V = 1/3 pi*r^2*h + 1/2 *4/3 * pi * r^3
=> V = 1/3 * 22/7 * 1.5^2 * 4.5 + 1/2 * 4/3 * 22/7 * 1.5^3
= 10.6071 + 7.07143
= 17.7 inch^3
And who is the one that does not agree with me?